Heat butter in a large pan over medium heat. Add garlic, ginger paste, and green chillies. Sauté 30 seconds until fragrant.
Add onion and cook until soft and translucent, 4–5 minutes.
Add tomatoes and cook 2–3 minutes until jammy.
Stir in bell pepper and green peas. Cook 2–3 minutes, keeping a little bite in the pepper.
Add mashed potatoes and a small pinch of salt. Cook 2–3 minutes, mashing gently.
Fold in crumbled paneer and minced beetroot. Cook 2–3 minutes until uniform and tinted that classic pav bhaji red.
Lower the heat. Stir in sour cream and cottage cheese until smooth.
Add about ¾ cup shredded cheese (reserve the rest for topping). Pour in milk a little at a time until thick and scoopable, not soupy.
Add turmeric, red chilli powder, cumin powder, coriander powder, and pav bhaji masala. Sauté 1 minute. Stir in cilantro, taste, and adjust salt.